Utilizing Excel's turing capabilities to create Conway's 'Game of Life'

Patrick2788 

You have prompted me to have another go.  I have made some minor changes to your solution such as using REDUCE rather than recursion and a DROP/TAKE combination to isolate neighbourhoods.

The fun step was then to switch REDUCE to SCAN and produce the result as an array of thunks.  That allows the user to iterate the board in place or display the entire sequence of results.

Worksheet formula
= LET(
    result, SCAN(THUNK(board), SEQUENCE(generations), Stepλ),
    EVALTHUNKARRλ(IF(ShowAll, result, TAKE(result,-1)))
  )


//A simulation of Conway's Game of Life
Stepλ 
=LAMBDA(gridϑ, k,
    LET(
        grid, gridϑ(),
        life, MAKEARRAY(
            ROWS(grid),
            COLUMNS(grid),
            LAMBDA(r, c,
                LET(
                    border?, OR(r=1, c=1, r=ROWS(grid), c=COLUMNS(grid)),
                    // Identify neighbourhood and cell state
                    neighbourhood, TAKE(DROP(grid, r - 2, c - 2), 3, 3),
                    alive, INDEX(neighbourhood, 2, 2),
                    //total the neighbours
                    count, SUM(neighbourhood) - alive,
                    //cell has 3 neighbors or is alive and has 2 neighbors - keep
                    IF(border?, "x",  alive * (count = 2) + (count = 3))
                )
            )
        ),

    THUNK(life))
);